Least Common Multiple of 192 and 196

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 192 and 196 the smallest integer that is 9408 that is divisible by both numbers.

Least Common Multiple (LCM) of 192 and 196 is 9408.

LCM(192,196) = 9408

LCM of 192 and 196

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 192 and 196

LCM of 192 and 196 is 9408

Least common multiple can be found by multiplying the highest exponent prime factors of 192 and 196. First we will calculate the prime factors of 192 and 196.

Prime Factorization of 192


2 192
2 96
2 48
2 24
2 12
2 6
3 3
1

Prime factors of 192 are 2,3. Prime factorization of 192 in exponential form is:

192 = 26×31

Prime Factorization of 196


2 196
2 98
7 49
7 7
1

Prime factors of 196 are 2,7. Prime factorization of 196 in exponential form is:

196 = 22×72

Now multiplying the highest exponent prime factors to calculate the LCM of 192 and 196.

LCM(192,196) = 26×31×72
LCM(192,196) = 9408

Factors of 192

List of positive integer factors of 192 that divides 192 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192

Factors of 196

List of positive integer factors of 196 that divides 196 without a remainder.

1, 2, 4, 7, 14, 28, 49, 98, 196

Least Common Multiple of 192 and 196 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 192 and 196, than apply into the LCM equation.

GCF(192,196) = 4
LCM(192,196) = ( 192 × 196) / 4
LCM(192,196) = 37632 / 4
LCM(192,196) = 9408

Properties of LCM 192 and 196

(i) The LCM of 196 and 192 is associative

LCM of 192 and 196 = LCM of 196 and 192

Related Least Common Multiples of 192

Related Least Common Multiples of 196

Frequently Asked Questions on LCM of 192 and 196

1. What is the LCM of 192 and 196?

Answer: LCM of 192 and 196 is 9408.

2. What are the Factors of 192?

Answer: Factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192. There are 14 integers that are factors of 192. The greatest factor of 192 is 192.

3. What are the Factors of 196?

Answer: Factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, 196. There are 9 integers that are factors of 196. The greatest factor of 196 is 196.

4. How to Find the LCM of 192 and 196?

Answer:

Least Common Multiple of 192 and 196 = 9408

Step 1: Find the prime factorization of 192

192 = 2 x 2 x 2 x 2 x 2 x 2 x 3

Step 2: Find the prime factorization of 196

196 = 2 x 2 x 7 x 7

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 9408 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 7 x 7

Step 4: Therefore, the least common multiple of 192 and 196 is 9408.